1. Field of the Invention
The invention relates to colloidal crystals, in particular formation of colloidal crystals useful as templates, e.g., for photonic band gap materials.
2. Discussion of the Related Art
Recently, there has been increasing interest in periodic dielectric structures, also referred to as photonic crystals (PC), in particular, photonic crystals exhibiting gaps in photonic band structures (referred to as photonic band gap (PBG) materials), for numerous photonic applications. See, e.g., P. S. J. Russell, xe2x80x9cPhotonic Band Gaps,xe2x80x9d Physics World, 37, August 1992; I. Amato, xe2x80x9cDesigning Crystals That Say No to Photons,xe2x80x9d Science, Vol. 255, 1512 (1993); and U.S. Pat. Nos. 5,600,483 and 5,172,267, the disclosures of which are hereby incorporated by reference. PBG materials exhibit a photonic band gap, analogous to a semiconductor""s electronic band gap, that suppresses propagation of certain frequencies of light, thereby offering, for example, photon localization or inhibition of spontaneous emission. A PC is generally formed by providing a high refractive index dielectric material with a three-dimensional lattice of cavities or voids having low refractive index. Photons entering the material concentrate either at the high-index regions or the low-index regions, depending on the particular energy of the photon, and the photonic band gap exists for photons of a particular energy between the two regions. Photons having energy within the PBG cannot propagate through the material, and their wave function thereby decays upon entering the material. The photonic band structure, therefore, depends on the precision of the physical structure and on its refractive index, and some difficulty has arisen in fabricating such materials. Specifically, it has been difficult to organize a three-dimensional lattice with micron-scale periodicities, particularly with high refractive index materials. (Micron-scale periodicities, as used herein, indicate that a structure contains repeating units, the repetition occurring at a distance falling within the range 0.1 xcexcm to 100 xcexcm.)
In one approach, reflected in the above-cited U.S. Patents, solid materials are provided with numerous holes by mechanical techniques, e.g., drilling, or by conventional silicon lithographic techniques. This approach has provided useful results, but is limited by the ability of current processing technology to provide the necessary structure. Drilling, for example, is not capable of providing periodicity on a micron scale. And conventional silicon lithography, for example, generally does not provide an article having sufficient dimensionality in all three dimensions.
In another approach, ordered colloidal suspensions or sediments of relative low refractive index particles such as silica or polystyrene, referred to as colloidal crystals, are used as templates for infiltration or deposition of high refractive index materials in a desired structure, and the particles are then etched away or burned out to provide the voids. Such crystals are typically formed by allowing slow sedimentation of substantially uniformly-sized particles in a liquid, such that the particles arrange themselves in a periodic manner. See, e.g., B. T. Holland et al., xe2x80x9cSynthesis of Macroporous Minerals with Highly Ordered Three-Dimensional Arrays of Spheroidal Voids,xe2x80x9d Science, Vol. 281, 538 (July 1998); E. G. Judith et al., xe2x80x9cPreparation of Photonic Crystals Made of Air Spheres in Titania,xe2x80x9d Science, Vol. 281, 802 (July 1998); and A. A. Zakhidov et al., xe2x80x9cCarbon Structures with Three-Dimensional Periodicity at Optical Wavelengths,xe2x80x9d Science, Vol. 282, 897 (October 1998). The infiltration/deposition has been performed, for example, by an alkoxide sol-gel technique and by chemical vapor deposition.
For this latter approach, the quality, e.g., uniformity, of the resultant material clearly relies significantly on the quality of the colloidal sediment. The lattice structure of such sediments generally exhibits two-dimensional periodicity, but not necessarily substantial three-dimensional periodicity. Specifically, sedimentation of the colloidal particles induces a random stacking with the close-packed planes perpendicular to gravity. Such a randomly-stacked structure does not exhibit substantial three-dimensional periodicity, because of the randomness in the gravity direction. It is possible that such materials will be suitable for some applications, e.g., filters and catalysts. However, for many photonic band gap applications, it is desired to have materials exhibiting substantial three-dimensional periodicity.
One reported way to provide improved uniformity of colloidal sediments is to use what is referred to as colloidal epitaxy to form the template crystal, as discussed in A. van Blaaderen et al., xe2x80x9cTemplate-directed colloidal crystallization,xe2x80x9d Nature, Vol. 385, 321 (January 1997), the disclosure of which is hereby incorporated by reference. Colloidal epitaxy involves growing a colloidal crystal normal to an underlying pattern, e.g., a series of holes, reflecting a particular face of a three-dimensionally ordered crystal, e.g., the (100) plane of a face-centered cubic (FCC) crystal. The holes are believed to order the first layer of settling colloidal particles in a manner that controls the further sedimentation. The holes are formed by electron beam lithography into a polymer substrate that serves as the pattern.
Colloidal epitaxy thus appears to be a useful process for improving the quality of colloidal crystals. Improvements, however, are continually sought.
The invention reflects a recognition that the template technique disclosed in van Blaaderen, supra, does not provide the expected level of three-dimensional periodicity. The invention therefore provides a process involving use of an improved template, by which extremely high-quality colloidal crystals are able to be formed.
Specifically, the template of van Blaaderen et al. is formed lithographically, as discussed above. As illustrated in the schematic cross-section of FIG. 1, the holes of van Blaaderen""s template 10 thus exhibit a cross-sectional structure having approximately 90xc2x0 angles between the hole walls 12 and the template surface 14. It has not been previously recognized that some of the colloidal particles settling onto this template tend to sit on the un-etched surface of the template, e.g., see particle 16, rather than falling into the lithographically formed holes. This phenomenon is believed to be due to concentration of electric fields at the sharp corners 18, which inhibits the particles from falling into the true minimum at the bottom of the holes. (Note that the technique of van Blaaderen appears to work well when using a solvent of glycerol and water and when viewing the sediment while wet. No dried crystal is examined in the van Blaaderen article. In fact, it is substantially impossible to attain a dried sediment with a glycerol/water solvent. As shown in Example 3 below, the van Blaaderen technique does not work as well as desired for a dried sediment.)
The invention avoids these problems by using a template 20 that substantially avoids such 90xc2x0 angles, as illustrated in the schematic cross-section of FIG. 2, such that the colloidal particles 22 are induced to settle into the desired locations. (The details of the template structure are discussed below.) The colloidal particles thereby settle in an ordered manner, making it possible to form colloidal crystals having substantial three-dimensional order.
In particular, a colloidal template of the invention (designed in this case for square geometry) is characterized by the following: for a drop (about 50 xcexcL) of an aqueous solution containing 4 wt. % colloidal silica spheres placed onto the template and allowed to dry, the resulting structure will show one or more layers of the spheres in a close-packed square geometry in registry with the underlying template (possibly with some vacancies present), with the alignment and spacing of the square lattice maintained across the template surface. (The presence of vacancies in this geometry is possible due to the small amount of solution, but does not negatively reflect on the quality of the template.) See, e.g., Examples 1 and 2, and FIG. 4. This high level of order allows formation of similarly-ordered subsequent layers, leading to a colloidal crystal having substantial three-dimensional order.
In one embodiment, the colloidal template of the invention is formed by a holographic method. Specifically, this embodiment involves spinning a photoresist onto a substrate, exposing the photoresist with crossed laser beams to generate a 1-D grating, rotating the substrate 90xc2x0, and exposing the photoresist again with crossed laser beams to generate a 2-D square grating. The photoresist is then developed to generate the desired surface relief pattern, a polymeric mold is made from the photoresist pattern, and the pattern is then cast in a curable optical adhesive. Other techniques for attaining the desired template characteristics are also possible.